Semiconductor circuits for generating reference potentials with predictable temperature coefficients

ABSTRACT

A positive-temperature-coefficient difference between the emitter-to-base potentials of two transistors in particular configuration is scaled up and added to one of the emitter-to-base potentials to develop a potential, a multiple of which is supplied as the reference potential.

Circuits are known for generating reference potentials related to V_(g)(0), the band-gap potential of a semiconductor material such as silicon, extrapolated to zero Kelvin. They may be particularly suited to fabrication in integrated circuit form. See R. J. Widlar's article, "New Developments in IC Voltage Regulators" appearing on pp. 2-7 of IEEE Journal of Solid State Circuits, Vol. SC-6, No. 1, February 1971, and K. E. Kuijk's article "A Precision Reference Voltage Source" appearing on pp. 222-226 of IEEE Journal of Solid State Circuits, Vol. SC-8, No. 3, June 1973. See, too, U.S. Pat. Nos. 3,271,660 (Hilbiber), 3,617,859 (Dobkin etal.), 3,648,153 (Graf) and 3,887,863 (Brokaw).

The present invention is embodied in a reference potential generator with superior potential regulation properties. While not restricted thereto, a number of embodiments of the invention are suitable for generating potentials related to V_(g)(0).

In the drawing:

EACH OF FIGS. 1, 2, 3, 5 and 6 is a schematic diagram of a reference potential generator furnishing a reference potential substantially equal to the V_(g)(0) of the semiconductive material from which its transistors are fabricated;

FIG. 4 is a block schematic diagram showing how the circuits of FIGS. 1, 2 and 3 may be modified to increase the reference potential by a factor m; and

FIG. 7 is a block schematic diagram showing how the circuits of FIGS. 5 and 6 may be modified to increase the reference potential by a factor m.

Each of the FIGS. 1, 2, 3, 5 and 6 includes first and second transistors Q₁ and Q₂, respectively, and first, second and third resistive elements R₁, R₂ and R₃, respectively. Each also includes first, second and third terminals T₁, T₂ and T₃, respectively. Q₁ and Q₂ are operated at the same absolute temperature T expressed in units Kelvin. Q₁ and Q₂ have respective base-emitter junctions with similar profiles and respective effective areas in l:p ratio, p being a positive number, as indicated by the encircled numbers near their respective emitter electrodes.

In FIG. 1, a bias means comprising the series connection of battery B₁ supplying potential V_(CC) and resistor R₄ tends to keep terminal T₄ (and terminal T₂ connected thereto) at a different potential from terminal T₁. A degenerative feedback connection is provided wherein V₂₁, the difference in potential between T₁ and T₂, is coupled via R₃ to terminal T₃ at the base electrode of transistor Q₃. The feedback biases Q₃, which has its emitter electrode connected to T₁, into conduction. The resultant collector-to-emitter current demand presented by Q₃ is met from battery B₁, with the collector current I_(CQ3) of Q₃ causing a potential drop across R₄ that reduces the potential V₄₁ between T₁ and T₄ to carry out shunt potential regulation of V₂₁. This degenerative feedback connection would--were the connection comprising Q₁, Q₂, R₁ and R₂ not present--operate to reduce V₂₁ to a value equal to the emitter-to-base potential V_(BEQ3) of Q₃ required to support a collector current flow substantially equal to (V_(CC) - V_(BEQ3))/R₄ --e.g., somewhere from 500 to 700 millivolts.

The connection comprising elements Q₁, Q₂, R₁ and R₂ provides for a regenerative feedback connection in addition to the degenerative feedback connection described. At low values of V₂₁, the regenerative feedback connection has sufficient gain to overwhelm the effects of the degenerative feedback connection. But as V₂₁ is increased, the gain of the regenerative feedback connection is reduced, and at some predictable value of V₂₁, the degenerative and regenerative feedback connections are so proportioned that the Nyquist criterion for stable equilibrium is met.

At low values of V₂₁, very little current will flow through the series combination of R₂ and Q₁ (regarded as a self-biased transistor). The portion of this current flowing through R₁ will cause a negligibly small potential drop across R₁, so the emitter-to-base potentials of Q₁ and Q₂ will be substantially equal. Current mirror amplifier action will thus obtain between transistors Q₁ and Q₂. The collector current I_(CQ2) of Q₂ will accordingly be about p times as large as the collector current I_(CQ1) of Q₁, the major component of the current flowing through the series combination of R₂ and Q₁ (regarded as a self-biased transistor). Any increase of V₂₁ above V_(BEQ1) will cause a current (V₂₁ - V_(BEQ1))/R₂ to flow through R₂, the major portion of which current will flow as I_(CQ1). I_(CQ2) will be about p times as large as I_(CQ1) --i.e., p (V₂₁ - V_(BEQ1))/R₂ -- causing a potential drop V₃₂ across R₃ substantially equal to p(V₂₁ - V_(BEQ1))R₃ /R₂. So, if pR₃ /R₂ be substantially larger than unity, increasing V₂₁ will decrease rather than increase the potential V₃₁ appearing between terminals T₁ and T₃ and applied as base-emitter potential to Q₃. Conduction of Q₃ will be suppressed, permitting V₂₁ to grow towards its upper limit value of V_(CC).

At higher values of V₂₁, the current (V₂₁ - V_(BEQ1))/R₂ through R₂ increases. The major portion of this current flows as I_(CQ1) through R₁ to cause a potential drop across R₁. For each 18 millivolts of drop across R₁, I_(CQ2) is reduced by an additional factor of two compared to I_(CQ1). So, while I_(CQ2) as well as I_(CQ1) increases with increasing V₂₁, its increase is slower than that of I_(CQ1). I_(CQ1) increases almost linearly with increasing V₂₁, and it will be shown that I_(CQ2) increases substantially less than linearly with increasing V₂₁. The current flowing from T₂ to T₃ via R₃ has a value (V₂₁ - V_(BEQ3))/R₃ and so increases substantially linearly with increasing V₂₁, at some value of V₂₁ overtaking I_(CQ2) in amplitude sufficiently to provide substantial base current to Q₃. This base current renders Q.sub. 3 conductive to carry out shunt regulation of V₂₁ against further increase.

Consider now why I_(CQ2) increases substantially less than linearly with increasing V₂₁. The operation of transistors Q₁ and Q₂ can be expressed in terms of the following expressions, as is well-known.

    V.sub.BEQ1 = (kT/q)ln(I.sub.CQ1 /A.sub.Q1 J.sub.S)         (1)

    v.sub.beq2 = (kT/q)ln(I.sub.CQ2 /A.sub.Q2 J.sub.S)         (2)

where V_(BEQ1) and V_(BEQ2) are the respective base-emitter junction potentials of Q₁ and of Q₂, k is Boltzmann's constant, T is the absolute temperature at which Q₁ and Q₂ are both operated, q is the charge on an electron, I_(CQ1) and I_(CQ2) are the respective collector currents of Q₁ and of Q₂, A_(Q1) and A_(Q2) are the respective effective areas of the base-emitter junctions of Q₁ and Q₂, and J_(S) is a saturation current density term presumed to be common to Q₁ and Q₂. At lower levels of input current applied to terminal T₄, the collector current of Q₁ is commensurately low, so that the base potential of Q₁ is applied to the base electrode of Q₂, without substantial drop across resistance R₁ due to I_(CQ1). Eliminating V_(BE) between equations 1 and 2, I_(CQ2) /I_(CQ1) at very low levels of collector current can be shown to be as follows:

    (I.sub.CQ2 /I.sub.CQ1) = A.sub.Q2 /A.sub.Q1 = p            (3)

With increasing level of the input current, which I_(CQ1) is adjusted to equal, the drop V₁ across resistor R₁, essentially equal to I_(CQ1) R₁, is increased.

    V.sub.1 = V.sub.BEQ1 - V.sub.BEQ2                          (4)

substituting equations 1, 2 and 3, into equation 4, yields the following expression.

    (I.sub.CQ2 /I.sub.CQ1) = p exp.sup.-1 (qV.sub.1 /kT)       (5)

the potential drop V₂ across R₂ is caused primarily by the flow of I_(CQ1) and is equal to the difference between V₂₁ and V_(BEQ1).

    v.sub.2 = i.sub.cq1 r.sub.2                                (6)

    v.sub.2 = v.sub.21 - v.sub.beq3                            (7)

an expression for I_(CQ1) can be obtained by cross-solving equations 6 and 7.

    I.sub.CQ1 = (V.sub.21 - V.sub.BEQ3)/R.sub.2                (8)

v₁ is caused primarily by the flow of I_(CQ1).

    V.sub.1 = I.sub.CQ1 R.sub.1                                (9)

substituting equations 8 and 9 into equation 5, one obtains equation 10 describing I_(CQ2) in terms of V₂₁.

    i.sub.cq2 = p(V.sub.21 - V.sub.BEQ3)/R.sub.2 exp(R.sub.1 /R.sub.2)(V.sub.21 - V.sub.BEQ3)(q/kT)                                       (10)

the improved regulation characteristics of the reference potential generators built in accordance with the present invention are due to the very great percentage change in the current gain of the configuration comprising elements Q₁, Q₂, R₁ and R₂ and linking T₂ to T₃ to apply non-linear regenerative collector-to-base feedback to Q₃, responsive to small percentage changes in V₂₁. This percentage change in current gain with small percentage change in V₂₁ is substantially superior to the non-linear regenerative feedback configuration as used by Widlar and Brokaw, differing from that shown by R₁ being replaced by direct connection and by the emitter of Q₂ being provided an emitter degeneration resistance. The current amplifier comprising elements Q₁, Q₂, R₁ and R₂ is per se known from U.S. Pat. Nos. 3,579,133 (Harford) and 3,659,121 (Frederiksen), but its non-linear current gain properties are not made use of as in the present invention.

Consider now how V₂₁ may be regulated to be substantially equal to V_(g)(0) the bandgap potential, as extrapolated to zero Kelvin, of the semiconductor material from which Q₁, Q₂ and Q₃ are made. V_(g)(0) exhibits zero temperature coefficient and, assuming the transistors to be silicon transistors, has a value of about 1.2 volts. One can discern that the FIG. 1 reference potential generator is capable of synthesizing V_(g)(0) since V₂₁ is equal to the sum of the base-emitter offset potential of a transistor (Q₁) and a potential proportional to the difference in the base-emitter potentials of two transistors (the drop across R₂), such a summation being a known technique for synthesizing V_(g)(0). The potential drop across R₂ is proportional to the drop across R₁ since: R₁ and R₂ conduct substantially the same current, and the drop across R₁ is known to equal V_(BEQ1) - V_(BEQ2).

Knowing V_(CC) and what V₄₁ is to be in terms of V_(g)(0), one can select a value of R₄ in accordance with Ohm's Law to provide a convenient nominal value of operating current, respective portions of which flow to Q₃ as collector current I_(CQ3), through R₃, and through the series combination of R₂ and self-biased Q₁. V₂₁ will have a value substantially equal to 1236mV and V_(BEQ1) is about 550 - 700mV depending on I_(CQ1). So the potential drop V₂ across R₂ is about 540 - 690mV. R₂ can be calculated by Ohm's Law, dividing the 540 - 690mV drop by I_(CQ1). The potential drop V₁ across R₁ is typically chosen to be 60mV or so at equilibrium, so the scaling factor between R₁ and R₂ is not too large, this drop divided by I_(CQ1) yields a value of R₁ about one-tenth or so of R₂. Knowing the equilibrium value of the voltage drop across R₁, one knows the value of I_(CQ2) /I_(CQ1) in terms of p, from equation 5. If V₁ is 60mV, and p unity, I_(CQ2) will be one-tenth I_(CQ1). Assuming the potential drop across R₃ to be substantially all attributable to I_(CQ2) and to be substantially equal to V₂, one can calculate R₃ by Ohm's Law to be V₂ /I_(CQ2), which equals (V₂ /I_(CQ1))(I_(CQ1) /I_(CQ2)), which equals R₂ (I_(CQ1) /I_(CQ2)) or about 10 R₂. Such calculations yield values of R₁, R₂ and R₃ of 600, 5600 and 56000 ohms, respectively, for example, with R₄ chosen to supply an I_(CQ1) of 0.1mA, an I_(CQ2) of 0.01mA, and an I_(CQ3) of 0.1mA--i.e., a total of some 0.2mA.

The FIG. 1 reference potential generator has the shortcoming, acceptable in some applications but not in others, that it depends upon V_(BEQ3) being determinate to obtain good regulation of V₂₁.sup.. V_(BEQ3) changes by 18 millivolts for each doubling of its collector current, however, so if the current applied between T₁ and T₂ of the reference voltage generator changes, the regulation of V₂₁ will be affected. An improvement would be to provide a threshold voltage for sensing the potential between T₁ and the second end of R₃ that would be substantially less dependent upon the operating current supplied to the reference potential. It would also be desirable, if possible, to reduce the current loading upon T₃ posed by the shunt regulating device while at the same time increasing the transconductance of the shunt regulating device.

The present inventor observed that the regulated value of V₂₁ applied to the series combination of R₂ and self-biased Q₁ causes the collector current I_(CQ1) of transistor Q₁ to be quite well-regulated so the value of V_(BEQ2) is substantially independent of the operating current supplied to the reference potential generator of FIG. 1. FIG. 2 shows a reference potential generator taking advantage of this observation to provide improvements upon the FIG. 1 reference potential generator.

In FIG. 2, a differential input amplifier A₁, such as an operational amplifier, replaces Q₃ in combination with R₄ to provide the means for sensing when the potential between T₁ and T₃ exceeds a predetermined threshold value to generate a reference potential directly related to such excess. The threshold value is set by V_(BEQ1), which because of V₂₁ being regulated is of more determinate value than V_(BEQ3). Rather than measuring the potential between T₁ and T₃ directly, one does it indirectly by comparing the potentials between the base of Q₁ and T₃. This permits substantially greater freedom of design of the amplifier T₃ works into. A₁ may use Darlington transistors of FET's in its input stage to reduce loading on the base of Q₁ and on T₃, and one may readily use cascaded amplifier stages to secure very high transconductance in A₁ to improve the regulation of V₄₁.

FIG. 3 shows a reference potential generator that may be used instead of the FIG. 2 reference potential generator, in which V_(BEQ2) rather than V_(BEQ1) is used as the threshold value against which the potential at T₃ is compared. R₃ ' is equal to R₃ (R₁ + R₂)/R₁. Other modifications are possible in which the threshold value is between V_(BEQ1) and V_(BEQ2), being obtained from a point along R₁. Modifications of the FIG. 2 reference potential generator in which the inputs of A₁ are taken from taps on resistors R₂ and R₃ are also possible.

FIG. 4 shows a modification that can be made to any of the reference potential generators shown in FIGS. 1 through 3, which modification will increase the reference potential V₄₁ it produces by a factor m. This modification consists of a potential divider D₁ having an input terminal connected to T₄ and an output terminal connected to T₂. Potential divider D₁ divides the potential V₄₁ by a factor m to obtain the potential V₂₁ for application between T₁ and T₂.

FIGS. 5 and 6 show modifications of the reference potential generators of FIGS. 2 and 3, respectively, useful for providing V₂₄ reference potentials relatively negative, rather than relatively positive, as referred to a fixed potential shown as ground.

FIG. 7 shows a modification that can be made to either of the reference potential generators shown in FIGS. 5 and 6, which modification will increase the reference potential V₂₄ it produces by a factor m. This modification consists of a potential divider D₂ having an input terminal connected to T₄ and an output terminal connected to T₁. Potential divider D₂ divides the potential V₂₄ by a factor m to obtain the potential V₂₁ for application between T₁ and T₂.

In the circuits of FIGS. 2, 3, 5 and 6 as shown or as modified by FIGS. 4 and 7, R₄ may be omitted if A₁ is a conventional operational amplifier rather than an operational transconductance amplifier.

In the reference potential generators of the sort shown in FIGS. 2, 3, 5 and 6, the value of V₂₁ that exhibits a zero temperature coefficient will depart somewhat from V_(g)(0) depending upon the temperature coefficient of the resistors R₁, R₂ and R₃. The (V₂₁ - V_(BEQ1)) drop across R₂ of about 600mv will increase 1.75mV per Kelvin increase in temperature due to the negative temperature coefficient of V_(BEQ1) .sup.. So I_(CQ1), the major portion of the current through R₂, will be held substantially constant if R₂ has a positive temperature coefficient as expressed in percentage equal to that of the potential drop across it +1.75mV/k/600mv = +0.29%/K. Such temperature coefficients can be achieved with ion-implanted integrated resistors. But diffused resistors normally have lower positive temperature coefficients--e.g., +0.2%/K--causing the zero-temperature-coefficient value of V₂₁ to vw less than V_(g)(0) by thirty-five millivolts or so.

While the provision of a zero-temperature-coefficient reference potential V₄₁ (or V₂₄) equal to V_(g)(0) has been specifically treated in the foregoing specification, the reference potential generator configurations shown are useful for generating reference potentials having other temperature coefficients. These V₄₁ 's (or V₂₄ 's) may be negative-temperature-coefficient potentials that are a multiple of V₂₁ 's that range between V_(BEQ1) to V_(g)(0). Or these V₄₁ 's (or V₂₄ 's) may be positive-temperature-coefficient potentials that are multiples of V₂₁ 's larger than V_(g)(0). 

What is claimed is:
 1. A reference potential generator comprising:first and second and third terminals; bias means for tending to increase the potential between said first and said second terminals; first and second transistors of the same conductivity type, each having base and emitter electrodes with a base-emitter junction therebetween and having a collector electrode, each of their emitter electrodes being directly connected without substantial intervening impedance to said first terminal; a first resistive element having a first end which connects to the base electrode of said first transistor and having a second end which connects to the base electrode of said second transistor and has the collector electrode of said first transistor connected thereto; a second resistive element having a first end connected to said second terminal and having a second end connected to the first end of said first resistive element; a third resistive element having a first end connected to said second terminal and having a second end connected to a third terminal and to the collector electrode of said second transistor; means for sensing when the potential between said first and third terminals exceeds a predetermined threshold value to decrease the potential between said first and said second terminals, thereby to generate a reference potential; and means applying between said first and said second terminals a fixed portion of said reference potential, thereby completing a feedback loop for regulating said reference potential to prescribed value.
 2. A reference potential generator as set forth in claim 1 wherein said means for sensing when the potential between said first and said third terminals exceeds a predetermined threshold potential to generate a reference potential directly related to said excess senses the potential between said first and said third terminals directly and comprises:a third transistor of said same conductivity type having emitter and base electrodes respectively connected to said first terminal and to said third terminal, having a base emitter junction between its emitter and base electrodes, the offset potential of which corresponds to said predetermined threshold value, and having a collector electrode direct coupled to said second terminal.
 3. A reference potential generator as set forth in claim 1 wherein said means for sensing when the potential between said first and said third terminals exceeds a predetermined threshold potential to generate a reference potential directly related to said excess senses the potential between said first and said third terminals indirectly and comprises:a differential-input amplifier having an inverting input terminal connected to said third terminal, having a non-inverting input terminal to which a predetermined threshold potential related to at least one of the base potentials of said first and said second transistors is applied, and having output terminals between which said reference potential is supplied.
 4. A solid-state temperature-compensated voltage supply comprising:first and second transistors; a resistor connected between the base of said first transistor and the base of said second transistor; circuit mears for furnishing supply voltage to said two transistors to develop current flow therethrough with a current through said first transistor also flowing through said resistor; means for sensing the magnitude of the respective currents flowing through said two transistors; voltage-control means responsive to the currents sensed by said sensing means and operable to adjust the emitter potentials of said transistors to maintain the magnitude of said transistor currents at levels which provide a predetermined non-unity ratio of current densities within the two transistors responsive to which they exhibit a difference in their emitter-to-base offset potentials that is applied to said resistor connected between their bases to cause the current through said resistor to vary positively with respect to the temperature of said two transistors; means for developing a first voltage proportional to said resistor current and for combining said first voltage with a second voltage which varies negatively with respect to said temperature to produce a combined voltage having minimal overall variation with respect to said temperature; and output means coupled to said last named means and including an output terminal providing an output voltage proportional to said combined voltage.
 5. A voltage supply as claimed in claim 4, wherein said voltage-control means comprises:a high-gain amplifier serving as a comparator responsive to signals proportional to said current flows through said first and said second transistors to produce an output signal corresponding to the difference between said signals proportional to said current flows; and means coupling a voltage proportional to said output signal to the emitters of said transistors to drive the emitter potentials to values providing the desired ratio of current density in said transistors.
 6. A voltage supply as claimed in claim 5 wherein said sensing means comprises first and second load resistors connected in the collector circuits of said first and said second transistors, respectively.
 7. A voltage supply as claimed in claim 4 wherein the emitters of said first and said second transistors are connected together to provide equal emitter potentials. 